DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 29(2) (2009) 209-218
DOI: https://doi.org/10.7151/dmgt.1442

MULTICOLOR RAMSEY NUMBERS FOR SOME PATHS AND CYCLES

Halina Bielak

Institute of Mathematics
UMCS, Lublin, Poland
e-mail: hbiel@golem.umcs.lublin.pl

Abstract

We give the multicolor Ramsey number for some graphs with a path or a cycle in the given sequence, generalizing a results of Faudree and Schelp [4], and Dzido, Kubale and Piwakowski [2,3].

Keywords: cycle, path, Ramsey number.

2000 Mathematics Subject Classification: 05C55.

References

[1] S. Brandt, A sufficient condition for all short cycles, Discrete Appl. Math. 79 (1997) 63-66, doi: 10.1016/S0166-218X(97)00032-2.
[2] T. Dzido, Multicolor Ramsey numbers for paths and cycles, Discuss. Math. Graph. Theory 25 (2005) 57-65, doi: 10.7151/dmgt.1260.
[3] T. Dzido, M. Kubale and K. Piwakowski, On some Ramsey and Turán-type numbers for paths and cycles, Electr. J. Combin. 13 (2006) R55.
[4] R.J. Faudree and R.H. Schelp, Path Ramsey numbers in multicolorngs, J. Combin. Theory (B) 19 (1975) 150-160, doi: 10.1016/0095-8956(75)90080-5.
[5] A. Figaj and T. Łuczak, The Ramsey number for a triple of long even cycles, J. Combin. Theory (B) 97 (2007) 584-596, doi: 10.1016/j.jctb.2006.09.001.
[6] Y. Kohayakawa, M. Simonovits and J. Skokan, The 3-colored Ramsey numbers of odd cycles, Electr. Notes Discrete Math. 19 (2005) 397-402, doi: 10.1016/j.endm.2005.05.053.
[7] D.R. Woodall, Maximal circuits of graphs I, Acta Math. Acad. Sci. Hungar. 28 (1976) 77-80, doi: 10.1007/BF01902497.

Received 13 December 2007
Revised 4 July 2008
Accepted 23 October 2008


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